Oscillation Theorems for Second-Order Emden-Fowler Delay Difference Equations with a Sublinear Neutral Term

2020 ◽  
Vol 29 (12) ◽  
Author(s):  
V. S Shobha ◽  
S Tamilvanan ◽  
John R Graef ◽  
E Thandapani
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Neutral Term ◽  
Oscillation Theorems ◽  
Delay Difference Equations ◽  
Delay Difference

Oscillation theorems for second-order delay difference equations with superlinear neutral terms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Said R. Grace ◽  
John R. Graef
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
New Approach ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Oscillation Theorems ◽  
Delay Difference Equations ◽  
Delay Difference

Abstract Oscillation criteria for a class of second-order delay difference equations with a superlinear neutral term are established using a new approach. The results improve and significantly simplify the ones reported in the literature.

Improved oscillation criteria for second order nonlinear delay difference equations with non-positive neutral term

2016 ◽  
Vol 56 (1) ◽  
pp. 155-165 ◽  
Author(s):  
E. Thandapani ◽  
S. Selvarangam ◽  
R. Rama ◽  
M. Madhan
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Second Order ◽  
Delay Difference Equation ◽  
Oscillation Criteria ◽  
Neutral Term ◽  
Positive Integers ◽  
Delay Difference Equations ◽  
Delay Difference ◽  
Nonlinear Delay

Abstract In this paper, we present some oscillation criteria for second order nonlinear delay difference equation with non-positive neutral term of the form $$\Delta (a_n (\Delta z_n )^\alpha ) + q_n f(x_{n - \sigma } ) = 0,\;\;\;n \ge n_0 > 0,$$ where zn = xn − pnxn−τ, and α is a ratio of odd positive integers. Examples are provided to illustrate the results. The results obtained in this paper improve and complement to some of the existing results.

scholarly journals Nonoscillation of Second-Order Dynamic Equations with Several Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-34 ◽  
Author(s):  
Elena Braverman ◽  
Başak Karpuz
Keyword(s):  
Differential Equations ◽  
Difference Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Comparison Theorems ◽  
Nonoscillatory Solutions ◽  
Several Delays ◽  
Delay Differential ◽  
Delay Difference Equations ◽  
Delay Difference

Existence of nonoscillatory solutions for the second-order dynamic equation(A0xΔ)Δ(t)+∑i∈[1,n]ℕAi(t)x(αi(t))=0fort∈[t0,∞)Tis investigated in this paper. The results involve nonoscillation criteria in terms of relevant dynamic and generalized characteristic inequalities, comparison theorems, and explicit nonoscillation and oscillation conditions. This allows to obtain most known nonoscillation results for second-order delay differential equations in the caseA0(t)≡1fort∈[t0,∞)Rand for second-order nondelay difference equations (αi(t)=t+1fort∈[t0,∞)N). Moreover, the general results imply new nonoscillation tests for delay differential equations with arbitraryA0and for second-order delay difference equations. Known nonoscillation results for quantum scales can also be deduced.

Sign in / Sign up

Export Citation Format

Share Document